Step by step
The question
Question: find (f + g)(2) for f(x) = 2x + 1 and g(x) = x − 3.
f(x) = 2x + 1
g(x) = x − 3
(f + g)(x) means f of x plus g of x.
We add the two answers.
(f + g)(x) = f(x) + g(x)
1 Work out f(2)
Put 2 in place of x in f.
We write it in brackets.
f(2) = 2(2) + 1
Times comes before plus.
Order: ( ) → x² √ → × ÷ → + −
2(2) = 2 × 2
2(2) means 2 times 2.
2 times 2 is 4.
= 4 + 1
4 plus 1 is 5.
f(2) = 5
2 Work out g(2)
Put 2 in place of x in g.
g(2) = 2 − 3
We take away more than we have.
Start at 2.
Go down 3.
We pass 0 and land on −1.
g(2) = −1
3 Add them
f(2) plus g(2): 5 + (−1).
(f + g)(2) = 5 + (−1)
So (f + g)(2) = 4.
(f + g)(2) = 4
4 Check
Let's check another way.
First the whole rule: (f + g)(x) = 3x − 2.
(f + g)(x) = 3x − 2
Then put in 2.
We get 4 again.
It works!
(f + g)(2) = 3(2) − 2 = 6 − 2 = 4
Let's look back.
First: work out f(2).
Then: work out g(2).
Then: add them.
Last: check.
Answer
(f + g)(2) = 4